One of the Democratic contenders said Tuesday that the fourth-term Democratic mayor told him just that in a private conversation.

Speaking at a luncheon sponsored by WisPolitics and the Milwaukee Press Club, Democratic gubernatorial candidate Matt Flynn said he saw Barrett at a luncheon last week and that the Milwaukee mayor said he will not seek the Democratic nomination for governor.

Flynn, the former state Democratic Party chief, quoted Barrett as saying, "You’ve got nothing to worry about from me. I’m not running."

But Barrett, who has lost three bids to be the state's CEO, declined to confirm that he is sitting out the contest, even though that is becoming obvious to anyone familiar with Wisconsin politics. If he runs, he would need to submit his nomination papers by June 1.

Speaking to reporters after a news conference Tuesday, the mayor said he is still weighing his options.

"I have not made a decision," Barrett said. "Obviously, the clock is ticking very quickly. The nomination papers are due June 1. So obviously I'll make an announcement before then."

But even some of Barrett's key supporters say it's time to pull the plug.

"He has not told me he's not running," a source said. "But he could find zero encouragement."

Behind the scenes, Barrett has expressed concerns about the quality of Democratic candidates.

In the most recent Marquette University Law School Poll, state schools superintendent Tony Eversled the pack of Democratic contenders with 18% of the vote. Madison Mayor Paul Soglin was at 9%. Forty-four percent of those polled said they don't know who they'll vote for.

On top of that, none of the nine notable Democratic gubernatorial candidates is raising big bucks.

Barrett, by contrast, is sitting on at least $622,000 in his campaign fund and has shown an ability to raise money quickly in the past.

And this could very well be a good year for Democrats. Insiders are emboldened by a recent Public Policy Polling survey that found Gov. Scott Walker down five percentage points to a generic Democratic candidate.

Those close to Barrett say he is also concerned about how poorly Madison has treated Milwaukee under Walker's leadership, pointing to a host of issues including lifting residency requirements for city workers, efforts to limit the streetcar and cuts in state aid. The mayor has told his advisers he might be able to do more for Wisconsin's largest city as governor.

When it first surfaced that Barrett, who has lost twice to Walker, was considering a run, Flynn offered pointed criticism.

"Tom's obviously formidable, and if he'd gotten into the race a year ago, people would take that into account," said Flynn, who has himself lost four election bids. "But people are pretty well coalescing around different candidates."

At Tuesday's WisPolitics event, Flynn said he spotted Barrett at lunch the other day and talked to him about that remark.

"He's an old friend of mine," Flynn told reporters Tuesday. "So I went up to him and said, 'Tom, look — we're friends, and I was kidding around.' He said, 'You have nothing to worry about from me.' And he said, 'I'm not running.'"